We've seen planes create a fiery vortex in the sky before, but here's a more peaceful version of it happening in real time. It's majestically beautiful. The wingtip vortices formed when an Airbus A340 landed at Zurich Airport on a foggy night. Though it looks gorgeous, vortices can be pretty dangerous.
Wingtip vortices occur because of the difference in pressure between the upper and lower surfaces of a wing. The air in the upper and lower start swirling to create a vortex of sorts. Those vortices eventually disappear but can also cause downflow behind the wing and form wake turbulence (turbulence behind the aircraft). The great internet encyclopedia says:

Wake turbulence is especially hazardous in the region behind an aircraft in the takeoff or landing phases of flight. During take-off and landing, aircraft operate at high angle of attack. This flight attitude maximizes the formation of strong vortices. In the vicinity of an airport there can be multiple aircraft, all operating at low speed and low height, and this provides extra risk of wake turbulence with reduced height from which to recover from any upset.